Black Hole Binding Energy Radiation

I don't know whether this is more appropriate forum than the astrophysics as far as the black holes are conserned... Anyway

I would like to know what happens to the binding energy when a black hole eats an object? It is necessary to radiate it in order the object would not escape. However, everybody reports that nothing besides the Hawking radiation (temperature is inverse proportional to mass) escapes the black hole. Is it right to think that the added mass increases the Hawking radiation (the linear drop in temperature is compensated by the larger hole square) and the binding enerty escapes in this form?

According to standard theory, any energy that falls into a black hole simply ends up contributing to its overall energy (and the corresponding mass). The overall energy of the falling object includes any internal energy corrections (such as positive thermal energy or negative binding energy) within a composite object.

Despite my failure to understand Jonathan's writing, I think I understand the process now. As some object falls onto a massive body, it accelerates until the center of attraction. The potential energy of gravity is transformed into kinetic energy of speed. The body then flies away while slows down (kinetic-to-potential back transform). In order to prevent the fly away, the falling object must be bound (smashed) to the planet. Normally, this is done by dissipating the kinetic energy, which is later radiated in the form of heat. As long as Hawking is not concerned, it is not radiated in case of BH. That's simple.

The kinetic theory tells that the particles in thermal motion occasionally get enaugh energy to escape the attractor. The probability is proportional to the ratio between the internal kinetic energy (the temperature) and the binding potential energy: P = exp(W/kT). When the ratio is positive, the probability is higher than 1 - the particle must escape the potential hole.

The object attracted by a planet is accelerated and has the right energy to escape the planet when it hits it. Even if does not escape, it adds to the planet temperature, thus reducing its binding energy. The extra energy contributed might be so high that the binding energy of the planet is exceeded -- something must fly away. So is with the planet = BH.

BTW, even the fact that a BH particle cannot escape from BH to infinity does not mean it cannot show up at any distance behind the BH radius.